Problem: Solve for $x$ and $y$ using elimination. ${-6x-2y = -26}$ ${-5x+2y = -7}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-11x = -33$ $\dfrac{-11x}{{-11}} = \dfrac{-33}{{-11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-6x-2y = -26}\thinspace$ to find $y$ ${-6}{(3)}{ - 2y = -26}$ $-18-2y = -26$ $-18{+18} - 2y = -26{+18}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {-5x+2y = -7}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ + 2y = -7}$ ${y = 4}$